Francois Hollande becomes France's new president
Francois Hollande has been sworn in as president of France, becoming the first Socialist leader in 17 years to occupy the Elysee Palace.
He said he was aware of the challenges ahead, including the debt crisis, and vowed to "open a new path in Europe".
He named close aide Jean-Marc Ayrault as his PM. Mr Hollande is now to visit Chancellor Angela Merkel in Berlin.
Mr Hollande called for "a compromise" over the German-led focus on austerity as the way out of the eurozone crisis.
Stock markets and the euro have fallen amid continuing political uncertainty in Greece.
The handover of presidential power in France is a strange mixture of tradition and improvisation. There is tradition in the quasi-monarchical ceremonies, such as the presentation of the gold Legion of Honour chain.
But the Fifth Republic is still a youngish institution, and much is left to the incoming head of state to choose how to run his day.
Francois Hollande wanted to present a new, modest, sober image of the presidency. So his four children and other family members were notably absent from the Elysee (a deliberate contrast with Nicolas Sarkozy's investiture).
And then in the afternoon the new president paid visits to memorials in Paris dedicated to two of his personal heroes: the late 19th-Century reformer Jules Ferry and the scientist Marie Curie.
Ferry is honoured for founding the Republican school system - though unkind souls have also pointed out that he was also a pillar of French colonialism!
All in all, Inauguration Day is an odd kind of day for any new French president, not helped in Mr Hollande's case by the awful weather. By the end, everyone is impatient to get down to business. Which is just as well, given the state of European affairs.
The chairman of the eurozone finance ministers, Jean-Claude Juncker, insisted on Monday night that they would do "everything possible" to keep Greece in the euro.'Message of confidence'
Mr Hollande was sworn in for a five-year term at the Elysee Palace in central Paris.
Outgoing President Nicolas Sarkozy shook hands with his successor in the palace's courtyard before leading him inside for a private meeting, at which France's nuclear launch codes were handed over.
The new leader asked that the inauguration ceremony be kept as low-key as possible, and invited just three dozen or so personal guests to join the 350 officials attending. Neither Mr Hollande's children nor those of his partner, Valerie Trierweiler, were there.
In his first presidential speech, Mr Hollande said he wished to deliver a "message of confidence".
"My mandate is to bring France back to justice, open up a new path in Europe, contribute to world peace and preserve the planet."
The new president said he was fully aware of challenges facing France, which he summarised as "huge debt, weak growth, reduced competitiveness, and a Europe that is struggling to emerge from a crisis".
Mr Hollande also said he wanted other European leaders to sign a pact that "ties the necessary reduction of deficit to the indispensable stimulation of the economy".
"I will tell them the necessity for our continent is to protect, in an unstable world, not only its values but its interests in the name of commercial exchange," he added.
After the inauguration, Mr Hollande rode up the Champs Elysees in an open-topped car, waving to the crowd despite the rain, before laying a wreath at the Tomb of the Unknown Soldier under the Arc de Triomphe.
He then paid tribute to the 19th-Century educational reformer Jules Ferry and the Nobel Prize-winning chemist Marie Curie.
The BBC's Christian Fraser in Paris says the 57-year-old has spent the past week preparing to take up the presidency, and now the work begins in earnest.
After the ceremonies, Mr Hollande named Jean-Marc Ayrault, leader of the Socialist group in parliament, as his prime minister.
Mr Ayrault, who is regarded as a Germanophile with good contacts in Berlin, had been widely tipped for the post.'Compromises'
On Tuesday afternoon, Mr Hollande will fly to Germany for dinner with Chancellor Merkel, who says she will welcome the new leader "with open arms".
But her embrace will hide some embarrassment, says the BBC's Europe editor Gavin Hewitt, after Mrs Merkel openly supported Mr Sarkozy in the election battle.
In Berlin there is suspicion of Mr Hollande. They do not like the fact that during the campaign he raised the standard against austerity and championed growth. Many saw that as a bid to reclaim French leadership in Europe”
"We don't think the same on everything," Mr Hollande acknowledged on French television on Monday. "We'll tell each other that so that together we can reach good compromises."
Mr Hollande has demanded that a European fiscal pact that cracked down on overspending be renegotiated to include a greater emphasis on measures to stimulate growth, while Germany insists the treaty must be respected.
Whatever their differences, the crisis in the eurozone will put them under huge pressure to compromise, our correspondent says.
As the eurozone's two biggest economies - and biggest contributors to its bailout funds - Germany and France are key decision-makers over the strategy supposed to pull Europe out of crisis.
According to official figures released on Tuesday morning, the French economy showed no growth in the first quarter of 2012. Growth in the final quarter of 2011 was also revised down to 0.1% from 0.2%.
However, Germany's economy grew by a stronger than expected 0.5% in the first three months of the year.
Following his German trip, Mr Hollande will hold his first cabinet meeting on Thursday followed by a visit to Washington to meet US President Barack Obama on Friday.